Bayesian Models for Dependence Between Continuous and Discrete Random Variables Using Conditional Copula

• Activity Number: 618
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Avideh Sabeti*+ and Radu Craiu
• Companies: University of Toronto and University of Toronto
• Keywords: Copula ; Bayesian Splines ; MCMC ; Conditional Copula ; Logistic Model ; Dependence Model

Abstract

Copula models have become an important tool in the statistician's toolbox as they are increasingly used for modeling survival, financial and actuarial data that exhibit complex dependence patterns. In statistics, the copula is a function that binds marginal distributions of a vector component into its multivariate distribution. The conditional copula models are applicable to conditional distribution functions and can be used naturally in regression settings. We propose a latent variable conditional copula model to represent the dependence between a binary and a continuous outcome. Since in many cases we do not know what functional dependence exists between the copula parameter and the co-variable, a flexible model will be used in which the relationship is defined by a linear combination of cubic splines. We propose posterior predictive copula selection procedures that use samples from the posterior distribution to select the appropriate model.